Algebraic and calculus concepts may be better way to introduce children to math - <AUTHOR> http://www.theatlantic.com/education/archive/2014/03/5-year-olds-can-learn-calculus/284124/ <comment><USER3> (Disclosure: I'll be working with Maria on the calculus series for kids.)

I'm a big fan of the conceptual approach. One of the largest problems I see with math education is that we don't check if things are really clicking.

I graduated with an engineering degree from a great school, and still didn't have an intuitive understanding for i (the imaginary number) until I was about 26.

Go find your favorite tutorial introducing imaginary numbers. Got it? Ok. It probably defines i, talks about its properties (i = sqrt(-1)) and then gets you cranking on polynomials.

It's the equivalent of teaching someone to read and then having them solve crossword puzzles. It's such a contrived example! (N.B., this anguish forced me to write a tutorial on imaginary numbers with actual, non-polynomial applications, like rotating a shape without needing trig. See [https://news.ycombinator.com/item?id=2712575](https://news.ycombinator.com/item?id=2712575))

Calculus needs these everyday applications and intuitions beyond "Oh, let's pretend we're trying to calculate the trajectory of a moving particle." They're out there: my intuition is that algebra gives a static description (here's the cookie), while calculus describes the process that made it: here's the steps that built the cookie. Calculus is the language of science because we want to know how the outcome was produced, not just the final result. d/dx velocity = acceleration means your speed is built up from a sequence of accelerations.

<comment><USER4> Yes, yes, yes.

I have tried (fitfully) three times to sit down and learn what calculus actually means. I still don't get it. And I suspect that clients and families will push it ever further away.

Yes, give me real world puzzles and applications for learning new mental tools and I will probably love them. Make it abstract enough and I cannot see the value in learning it.

<comment><USER3> I was the same way :). I have an intuition-first guide to calculus, here:

[http://betterexplained.com/calculus/lesson-1](http://betterexplained.com/calculus/lesson-1)

I think the essentials on how to think with calculus can be conveyed in 1 minute. Let me know if the above helps :).

<comment><USER5> I see that your examples of teaching fast (one minute, ten minutes) all use discrete models for continuous processes. For people who understand continuousness mathematically, going between discrete models to continuous models and vice versa is easy. However, there are indications that the other way around -- students who perceive these changing situations mathematically as intrinsically discrete -- going from discrete to continuous models might be extreme difficult (due to in-commensurability). Of course, students can learn procedures to make the switch from discrete to continuous models, but even then it is possible that this procedural experience is not build on deeper mathematical understanding. Tricky stuff, learning mathematics :-)

<comment><USER3> Great point, thanks for the comment.

I think the key missing insight for me was that a continuous process and a discrete process can both point to the same result.

A pixellated word on a screen ("cat") conveys the same meaning as a perfectly smooth vector of the same word. The math idea, to me, is "can a discrete description/process" point at the same result that we get from a continuous one?

The idea of limits, is essentially figuring out when a discrete epsilon can still lead us to the true value of f(x) (if this trick works, we call it a continuous function, and can use calculus with it.)

<comment><USER5> Yes. You might be interested in Cornu, B. (1991). Limits. In D. Tall (Ed.), Advanced Mathematical Thinking (Vol. 11, pp. 153–166). Retrieved from [http://dx.doi.org/10.1007/0-306-47203-1_10](http://dx.doi.org/10.1007/0-306-47203-1_10) and similar works. Volumes have been written about the limit concept, learning the limit concept, and different approaches to the limit. It is one of the more interesting mathematical concepts one encounters in high school, not in the least because of the ability to use it successfully without understanding the underlying concept and the philosophical implications of the concept.

Unfortunately, I doubt that these implications will be discussed in your average Mathematics classroom. Actually, my experiences with mathematics in primary, secondary and a lot of tertiary education, both as a student, teacher and observator, leads me to believe that conceptual discussion is rare, whilst procedural discussions (how to perform some calculation) are plenty and abound.

</comment></comment></comment></comment></comment></comment><comment><USER6> I love it. This really appeals to me because of the all the bad ideas I had to unlearn in my 20s:

\- math is about numbers and arithmetic operations on them \- being good at math meant you were good at arithmetic \- some people (meaning me) just didn't have what it took to be "good" at math. Reinforced by my high school math and physics teachers.

I hated math because I didn't understand that mathematics is a system for representing abstract concepts and manipulating them.

Eventually on my 4th try to get calculus, I took a class from nick fiori([http://www.yale.edu/education/about/faculty/fiori.elw062111](http://www.yale.edu/education/about/faculty/fiori.elw062111)).

His teaching methods opened my mind, and I've gone on since then to become an ardent amateur mathematician with minor publications and career tangents in machine learning and data science.

I can only imagine what would have happened if I had been taught math well from an early age.

<comment><USER7> Good to hear, any math books you'd recommend to someone who's not there yet, or remember from that class?

<comment><USER6> Sorry, did not learn much from books. The only one of note is the Tom Mitchell Machine Learning Book, which already requires a basic advanced mathematics fluency. I also believe it is a little out of date.

I can recommend a few professors who really opened my mind to how to use math, all at UCSC (CS grad school for me):

\- Dave Helmbold (Machine Learning) \- Kevin Ross (Operations Research) \- Martin Abadi (Security)

</comment></comment></comment><comment><USER8> Yes yes yes.

The mechanics of basic calculus are remarkably simple. After a while it becomes a game of sorts with a pretty simple set of rules. Once you learn to "see" parts of the equation as symbol blocks (instead of numbers needing computation), you can move them around freely so long as you follow the rules. Algebra is simply a subset of the rules.

Teaching kids to think symbolically will help them in so many other fields.

I'm pretty convinced that with a little thought, you can teach basic derivation and integration to pretty young kids. Carefully craft the problems to avoid difficult division problems, avoid trig, let them use lookup tables for multiplication and you _might_ be able to get kids under 10 to even do some of this.

Then "vertically integrate" other algebraic and trigonometric concepts into this framework, like adding new pieces to the game.

<comment><USER9> Hm, you're talking about teaching symbolic manipulation using calculus, but for me the real ideas of calculus are integration and derivation. I think those ideas are very valuable, and symbolic manipulation is just one way to solve those problems.

<comment><USER8> Can you provide some examples? To me, the basic mechanics I remember (for simple equations like x^3 d/dx) were almost entirely "solvable" by moving bits of the equation around...

1\. move the 3 in front of the x

2\. where the 3 was, subtract 1 from it and put that back where the 3 was

but if you think of it as symbols you get more like

1\. move the exponent symbol in front of the x symbol

2\. subtract 1 from that exponent and put it back where the original exponent symbol was

For me at least, bridging the gap from the specifics of the first example to the more generalized second approach meant that when I was given something like

3x^(y^4) d/dx my mind was absolutely blown because I didn't know if there was some rule I needed to know if the exponent had an exponent or something.

Going from the years of the arithmetic approach to really groking the symbolic manipulation approach was _really_ hard for me, and looking at lots of young kids suffering through algebra it was the same.

Learning how to recognize the symbols through the specificity of the numbers was something I don't think I really got at all until calculus and it's because the mechanics of the rules of simple derivatives and integration really force you to recognize the underlying symbols...more than algebra did (which for me just seems like a really complicated arithmetic rather than what's actually a pretty simple symbol manipulation exercise).

It's odd, because like most technically minded kids, I was already great working with symbols and breaking things down and building them up. I could build huge structures out of various small assemblies with legos, write simple software, crank out papers for English class that would guarantee an A and so on, but understanding that the teachers no longer wanted me to be a human tabulation device but to be a manipulator was something I never really cottoned on to.

I know from spending a little time with nieces and nephews younger then 10 that you can teach basic derivatives in about an hour or two and have them fairly reliably doing simple work like the above in an afternoon if you don't worry them too much about simplification of the result or all the arithmetic.

My _gut_ says that if you start adding more rules, like what do you do when you have something like (x^3)/(x^2) and how exponents should be subtracted, and with a little care in the examples you show them of this rule in action, you end up showing them all of algebra, fractions, exponents and later trig, logs, etc. while building up and hanging all of these concepts off of calculus.

TBH I don't know enough about early childhood education to know if this should be used _instead_ of basic arithmetic or not, but I bet if you use shapes and colors instead of letters and numbers and start to teach basic rules, you can just slowly introduce numeracy later anyways when their brains are more developed.

<comment><USER10> No offense, but what you're proposing would be a huge step backwards. All of those examples you've given are extremely special cases of a general concept, where the concept is relatively easy to understand (two points make a line, we only have one point, so take the limit) although the implementation is complex (requires either understanding algebra or knowing lots of rules.)

If you try to teach a little kid the power rule right off the bat, they will both be turned off of math (because it's just pushing x around for no clear reason) and have learned absolutely nothing of the important bits of calculus.

<comment><USER8> > where the concept is relatively easy to understand (two points make a line, > we only have one point, so take the limit) although the implementation is > complex (requires either understanding algebra or knowing lots of rules.)

The pedagogy of Mathematics education is fundamentally broken and we've lost generations of math users because of it.

Approaching it from this sense "two points make a line, we only have one point, so take the limit" _is_ the method today and with all respect, it's been a terrible terrible failure...even if it is "correct".

A few kids will grok it and turn into computer scientists or physicists or mathematicians of some sort, and the other 98% will take the bare minimum to get their high school education, and if they go on to college see which degree programs require math and which don't and select the B.A. degree that doesn't.

Anecdotal, but I don't know a single person who enjoyed their K-12 math education. I know lots of people who enjoy math, and found that joy in college or later, but found the educational experience of K-12 so abysmal and torturous that they completely swore off even pursuing fields with heavy Math components. There are lots of artists, musicians, writers and historians who would probably be great Mathematicians, Physicists and Scientists were it not for the piss poor job we do indoctrinating kids into math.

It's not just that students fail to learn mathematics, it's that the pedagogical experience is so negative that they swear off ever even trying. And IMHO, a very big part of that is the (to the student) endlessly pointless jargon filled inapplicable overly rigorous and formal mess that is Math education today.

I've sat in the audience on some very heated round tables about promoting STEM education in my region and I've come away convinced that getting more people into STEM is critical to long-term economic success, but students are not only _not_ drawn into STEM, they're actively driven away from it by the pedagogical approach of what amounts to a single class every year. Students love science classes and science labs, they love shop class and learning engineering, they love computers and everything else to do with STEM _except_ for the K-12 Mathematics education. And that loses them, it simply drives them away from all of these great (and often lucrative) fields.

More importantly, I think fields which are not traditionally Math focused, could benefit greatly from a better general Math education. Read a social sciences academic paper and see what I mean for a quick example.

> If you try to teach a little kid the power rule right off the bat, they will > both be turned off of math (because it's just pushing x around for no clear > reason) and have learned absolutely nothing of the important bits of > calculus.

I want to agree particularly with this, "it's just pushing x around for no clear reason". The fundamental problem with learning Mathematics in K-12 is applicability. Beyond arithmetic, students have almost zero examples of why they should bother learning anything else. _Most_ of the population gets by just fine without anything more complex than arithmetic and figuring out percentages (and even then that's a stretch).

When students go to their parents to seek guidance, their parents _also_ don't have any idea why they have to learn all this stuff. _They_ certainly don't need it in their day jobs and can't provide a hint as to why it's important other than the student needs to study it for the grades.

And to be honest, even if their parents _do_ use Mathematics in their work and can provide examples, it's likely that the student's ability to relate to that work is very limited. The reinforcement that all this time spent learning Math is pointless is much stronger than the reinforcement that it's important or useful. Getting a kid to crank through 20 or 30 algebra problems is _much_ harder than say, a 5 paragraph essay for English class because the entire time they're doing this they're saying to themselves "why am I doing this? Math is useless! At least learning to write a little has some kind of use!"

But children will play "pointless" games for hours and hours and hours - <USER2> not even ones they're especially having fun with, just ones that hold their interest (if you've ever watched a 9 year old vent frustration at their Xbox you'll know what I mean). If we can turn Mathematics education into a kind of "game", then fill in the details and formal bits as they age, they'll at least be able to relate to it even if they don't understand the application or relevancy.

And the truth is, once you get to Calculus and get it, it's actually pretty fun and pretty easy. That's a high enough discipline for most STEM jobs and I firmly believe that every K-12 student should be able to do what we call "college level" Calculus by the 10th grade. So why not try to capture the things that make Mathematics at that level fun and easy, and I think that's the symbolic manipulation, even if it is hard to establish relevancy, and get them used to doing it from a very early age. Kids can move blocks around and stack them before they can walk, why can't the blocks be bits of equations? And why can't moving the blocks have little game-like rules they can learn?

<comment><USER10> >Read a social sciences academic paper and see what I mean for a quick example.

I have actually done some graduate-level work in sociology and history, and the papers and books I read were mostly examples of very good statistical work and well-thought-out process analysis. You can put your STEM-master-race badge away.

>Beyond arithmetic, students have almost zero examples of why they should bother learning anything else.

When I say "for no reason," I don't mean "for no _day-to-day practical_ reason." Playing with abstract concepts is and should be its own reward; that was the whole point of TFA. Mechanically memorizing how to take the derivatives of polynomials is neither a fun abstract concept nor a boring-but- necessary practical skill.

>If we can turn Mathematics education into a kind of "game", then fill in the details and formal bits as they age, they'll at least be able to relate to it even if they don't understand the application or relevancy.

"Gamification" as a cynical ploy to get kids to sit still long enough memorize their times tables may or may not work. But even if it does, it's only gotten them to play the game long enough to pass them to the next level; it has deliberately shifted their interest away from the joy of learning for its own sake. That is __not __what the article is about, and it 's not helpful in the long run.

>Approaching it from this sense "two points make a line, we only have one point, so take the limit" is the method today and with all respect, it's been a terrible terrible failure...even if it is "correct".

No... no, it isn't. The approach today, for the majority of students, is to learn the bare basics so that you can plug them into an equation and find out what the marginal cost of widgets will be next year given a certain set of equations. And in any case, it comes so late that kids have been taught that "math" is something that actually _is_ boring and useless.

<comment><USER8> > Playing with abstract concepts is and should be its own reward

I'm sorry, but you're just simply wrong on all points. Promoting the status quo in math education, as you are doing, has been, is, and will continue to be a failure that drives kids away from learning. There are now decades of evidence of the failures of k-12 education to address this need and I find it unbelievable that you haven't gotten the picture yet.

I'm not saying that what I'm proposing is correct, but continuing the very poor pedagogical approach that you support is not going to solve the educational failures that we're experiencing today. What we need are fundamentally new approaches to Math education. You are not providing any insight into what those approaches should be.

I'm sorry, but in a discussion to fix and change what is obviously utterly broken in k-12 maths education, suggesting to just continue the course is not a helpful contribution and is simply part of perpetuating the problem.

This has been recognized for so long, that it has finally percolated out of educational establishment, which has failed to address the problem with undereducated and unqualified teachers, student motivation, repeated failures in curriculum development ( _Common Core_ is simply the latest joke of a curriculum), and has reached levels as high as the White House for targeting. You _have_ to know that the current approaches are failing if the President has to get involved.

From the "Report to the President...K-12 education in STEM" [http://www.whitehouse.gov/sites/default/files/microsites/ost...](http://www.whitehouse.gov/sites/default/files/microsites/ostp/pcast- stemed-report.pdf)

"Schools often lack teachers who know how to teach science and mathematics effectively, and who know and love their subject well enough to inspire their students. Teachers lack adequate support, including appropriate professional development as well as interesting and intriguing curricula."

"As a result, too many American students conclude early in their education that STEM subjects are boring, too difficult, or unwelcoming, leaving them ill-prepared to meet the challenges that will face their generation, their country, and the world."

"Put together, this body of evidence suggests that grade-school children do not think as simplistically about STEM subjects as conventional curricula assume. They are capable of grasping both concrete examples and abstract concepts at remarkably early ages. Conventional approaches to teaching science and math have sometimes been shaped by misconceptions about what children cannot learn rather than focusing on students' innate curiosity, reasoning skills, and intimate observations of the natural world."

[http://books.google.com/books?id=7v2gRGuxw4sC&pg=PA253&lpg=P...](http://books.google.com/books?id=7v2gRGuxw4sC&pg=PA253&lpg=PA253&dq=National+Research+Council.+\(2001\).+Adding+It+Up:+Helping+Children+Learn+Mathematics.+Washington,+DC:+National+Academies+Press&source=bl&ots=AgRbbDK-Z4&sig=kAkWvPXWg36IJ6wAynh- tpmfRtY&hl=en&sa=X&ei=7LYVU62RFePw0wGm7oHoAQ&ved=0CCYQ6AEwADgK#v=onepage&q=National%20Research%20Council.%20\(2001\).%20Adding%20It%20Up%3A%20Helping%20Children%20Learn%20Mathematics.%20Washington%2C%20DC%3A%20National%20Academies%20Press&f=false)

"The first principle of How People Learn emphasizes both the need to build on existing knowledge and the need to engage students' preconceptions -- particularly when they interfere with learning. In mathematics, certain preconceptions that are often fostered early on in school settings are in fact counterproductive. Students who believe them can easily conclude that the study of mathematics is 'not for them' and should be avoided if at all possible."

I differ from this report in that they continue to promote a bottom-up approach to maths education. I think math should be taught from a top-down approach, like nearly every other discipline. You don't learn to bake a cake by first spending 10 years learning about chemistry, agriculture, nutrition, animal husbandry, distillation etc. You say "I want to bake a cake" and you start with a simple cake recipe. Then the next time you say "I want to bake a different cake" and you use a more complicated recipe. And so on and so forth until you don't need a recipe and are putting together your own cakes from scratch.

The "cake" I'm proposing is calculus...and I believe, from experience teaching basic calculus to kids under 10, that this is realizable and beneficial.

The end result is that I don't expect kids to come out of K-12 baking cakes that look like this [http://www.askmamaz.com/wp-content/uploads/2013/01/Most- Beau...](http://www.askmamaz.com/wp-content/uploads/2013/01/Most-Beautiful- Wedding-Cakes-22.jpg)

when the average STEM work-a-day mathematics really requires them to do this.

[http://www.recipegirl.com/wp-content/uploads/2013/06/Red- Whi...](http://www.recipegirl.com/wp-content/uploads/2013/06/Red-White-and- Blue-Cheesecake-Cake-7.jpg)

Right now, your approach is producing students who don't even bother with cake baking, and when pressed into service produce this [http://fc05.deviantart.net/fs70/f/2012/070/1/b/ugliest_cake_...](http://fc05.deviantart.net/fs70/f/2012/070/1/b/ugliest_cake_ever_by_great_5-d4sfvj4.jpg)

This needs to change.

</comment></comment></comment></comment></comment></comment></comment><comment><USER11> A big secret in mathematics is that many ideas in mathematics are rather simple and straight forward.

Formulating and proving these ideas in a rigorous and logical manner, however, is the difficult part.

<comment><USER12> Explains my joy in puzzles and sequences. Sometimes I don't know why the next number in a series is. I used my intuition, arrived at the correct answer, and now the hard part is explaining myself.

</comment></comment><comment><USER13> This has, to some extent, been known for a long time. How many stories have you heard about math prodigies? I think the problem, though, is in that very sentence. Rather than considering whether this material might be more accessible than traditionally thought, we just assert outright that the child is a prodigy for learning calculus at a young age and then learn nothing from the observation.

I learned calculus in sixth grade and was and am very bad at arithmetic. It was easier for me to understand the fundamental theorem of calculus than it was for me to do long division in my head. I don't think I'm alone. I think I'm just among the few who, for one reason or another, actually made a serious attempt to learn the subject at the time.

<comment><USER14> > It was easier for me to understand the fundamental theorem of calculus than > it was for me to do long division in my head. I don't think I'm alone.

You're not. I had the same experience. I have severe problems with mundane arithmetic, my mind just locks up when faced with concrete numbers and even simple numerical calculations. OTOH, no problem whatsoever with geometry, (abstract) algebra, calculus etc. I remember when I first got calculus in high school, how natural and easy it felt, how it simply made sense and how all around pleasant and interesting it was, and it struck me how different this experience was to the other more "basic and mundane" areas I struggled with during school. A few years ago I was amused when I saw an interview with an astrophysics PhD who struggled with doing basic arithmetic. It's a source of amusement for her now, but you can imagine the dread she had to endure in "school". So, no, we're not alone.

What the article says when it compares what children face in school under the label of "mathematics" to torture akin to digging a trench with a spoon sounds very true to me.

</comment></comment><comment><USER15> The article headline is a little sensationalist. It's very rudimentary, and it's more about learning limits than equations. That said, games like DragonBox highlight that kids are capable of being introduced to these concepts well before schools get around to it.

<comment><USER16> My 5-yr-old played DragonBox a bit - first for the colourful critters and powering up her monster, but then for the problems.

It was pretty neat when I wrote down 2 + x = 7 and she was able to rearrange the equation to solve for x. (The later stages get considerably more complicated.) It's fantastic that kids think in terms of symbolic manipulation. Most adults still don't get that, and think maths is just about coming up with numbers.

<comment><USER15> I haven't figure out how to convert the on-line intuition into pen and paper. I saw a paper on their website. It still seems like a leap, when the kids haven't formally been taught multiplication, division and fractions. I'm glad that it worked in your case.

<comment><USER16> Hmm, have you tried having them do the actual problems on paper? No numbers or letters, just copy the screen onto paper:

Like write out:

      Side 1         |     Side 2
        Fly     Box  |   Mushroom

And have them solve into:

      Side 1         |     Side 2
        Box          |   Mushroom    Inverted Color Fly ("Dark Fly")

From there it's just a visual replacement to turn Box into x, Mushroom into a 7, and Fly into a 2. The game introduces "inverse color = -", so going from 2 to -2 should be a visual translation that doesn't actually require them to understand subtraction or inverse.

After they're all done, they _might_ notice "hey, wait, I recognize 7 -2 and it can also be written as 5!" But that's not relevant to manipulating the equation, is it?

Sure, without arithmetic they won't be able to calculate the most simple form (7 + -2 -> 5 or 2/4 + 3/6 -> 1) -- but that's a different skill. And people seem to have more issues with handling the equation than actually doing the arithmetic part.

</comment></comment></comment></comment><comment><USER12> Does anyone know of any resources to introduce math to a 6yo? I have apps like Dragonbox to introduce algebra to my son. He played with it, completed it, but now is back to the crap IAP games typical on tablets these days. I wouldn't mind a few more like Dragonbox.

I also use flashcards to help with the rote math homework.

<comment><AUTHOR> I don't ever use flashcards for mathematics learning. Not once, not ever. (I hardly use flashcards for foreign language vocabulary either, not even for Chinese characters, except for recognition of single characters in isolation, because there isn't any one-to-one correspondence of words between languages.) Working a lot of problems[1] eventually makes the math facts second-nature, without flash cards.

I do recommend to my children and my students that they consider doing one thing I did as a kid, namely fill out a multiplication table (the one I did in childhood was 30 × 30) by hand by hand calculation. I did that in odd moments during the school day and kept the table stashed in my desk between moments of working on it. Filling in a multiplication table helps learners notice number patterns (it made me very conscious of perfect squares, for example) and produces a tangible accomplishment at the end.

For a child the age of your child, I enthusiastically recommend the Miquon Math materials,[2] which are inexpensive and take a thoughtful, playful approach informed by higher mathematics for learning much of the content of the first several years of elementary mathematics. All you need to use with the Miquon Math books are Cuisenaire rods,[3] which are available from various sellers and are a fun plaything in themselves.

[1] [http://www.epsiloncamp.org/ProblemsversusExercises.php](http://www.epsiloncamp.org/ProblemsversusExercises.php)

[2] [http://miquonmath.com/](http://miquonmath.com/)

[3] [https://en.wikipedia.org/wiki/Cuisenaire_rods](https://en.wikipedia.org/wiki/Cuisenaire_rods)

<comment><USER12> Brilliant! thanks.

I did the multiplication as a child myself, only 20x20. I've also tasked him with the table, 10x10.

</comment></comment></comment><comment><USER17> Discussion on reddit: [http://www.reddit.com/r/math/comments/1zfizg/5yearolds_can_l...](http://www.reddit.com/r/math/comments/1zfizg/5yearolds_can_learn_calculus_why_playing_with/)

</comment><comment><AUTHOR> I see the article title (which I put on the submission, and one comment commented on) was replaced by an HN moderator with a rewording of the article subtitle. I guess that's okay.

The article was especially eye-catching for me, because it was first posted among our mutual Facebook friends by my mentor in homeschooling mathematics, the mother of the first United States woman to win a gold medal in the International Mathematical Olympiad. The teacher featured in the article as the developer of innovative teaching methods for young learners is also a Facebook friend of mine, and we are part of a network of parents and teachers who are curious about how to stimulate interest in mathematics among young learners by doing things differently from the United States typical school curriculum in mathematics. I'm grateful that my children have been exposed to approaches like that (which I follow imperfectly in my homeschooling my children and in teaching other learners in classroom courses for my occupation), as that has helped my oldest son launch into the adult world with good problem-solving skills for hacking at the startup where he works.

There is a continual tension in mathematics education between teaching topics in their logical order as we understand mathematical topics in light of modern higher mathematics and teaching topics in their historical order of development (which is largely what happens in school mathematics courses). Children need some concrete, tangible experience with counting and with shapes to understand much about mathematics. The cool abstractions that motivate higher mathematics may be inaccessible to children who have no experience with tangible examples of those absractions. (See

[http://www.latimes.com/opinion/commentary/la-oe-adv- frenkel-...](http://www.latimes.com/opinion/commentary/la-oe-adv-frenkel-why- study-math-20140302,0,5177338.story)

an article submitted to Hacker News yesterday, for more about this.) But it looks like we can gain in mathematics instruction by letting children play with more sophisticated representations of mathematics than most children get to play with. Games are great learning tools. One of favorite games for teaching mathematics I learned about from John Holt's book _How Children Fail_ (originally published 1964, which I read in 1971 on the advice of my school's assistant principal). The twenty questions game asks children to find a number from 1 to 1,000,000 by asking twenty yes/no questions, which the person who chose the unknown number must answer truthfully. It is an interesting mathematical exercise to show that twenty questions is (barely) enough for finding one number in one million if the twenty questions are used optimally. I have played this game many times with the children in my classes, and the opportunity to play this game again at the end of class is one of my strongest incentives for the children to stay focused during a lesson on a Saturday morning to get through the lesson content efficiently.

Playing with challenging problems appears to be the royal road for learning mathematics.

[http://www.epsiloncamp.org/ProblemsversusExercises.php](http://www.epsiloncamp.org/ProblemsversusExercises.php)

I hope ideas like this spread through many communities in the United States and the English-speaking world, so that more young people gain more opportunity to learn to enjoy challenging mathematics early and often.

<comment><USER18> As for math games, I can recall a few interesting examples:

Algebra for children: [http://www.wired.com/geekdad/2012/06/dragonbox/all/](http://www.wired.com/geekdad/2012/06/dragonbox/all/)

Interactive tutorial for sequent calculus: [http://logitext.mit.edu/logitext.fcgi/tutorial](http://logitext.mit.edu/logitext.fcgi/tutorial)

Ancient Greek Geography: [http://sciencevsmagic.net/geo/](http://sciencevsmagic.net/geo/)

<comment><USER19> DragonBox on iOS is pretty good at teaching algebra. [http://dragonboxapp.com](http://dragonboxapp.com)

</comment></comment></comment><comment><USER20> I know that when I learned calculus the hardest part was reconciling the notion of infinitesimals with algebra. The delta/epsilon definition of a limit was unsettling. It's a shame. Much of calculus is easy to grasp intuitively - Riemann integration is easy to see and explain.

<comment><USER21> Yes, the concepts of limits and derivatives are simple and intuitive, but the concept of the epsilon/delta proof just completely soars over students heads. I didn't learn the epsilon/delta stuff until _after_ all that other stuff, and I don't feel like it was the wrong order of things.

That and the prof I had never just really explained that epsilon just means "really insanely small" which probably would've helped.

<comment><USER22> I had to learn the epsilon-delta definition before I really understood limits. As far as insanely small goes, as you must know, the definition is equivalent to "for every epsilon < M, there exists a delta >0, ..." where M is some positive constant (it could be 1 or 1/10^100...). Sometimes it helps to play with the quantifiers...

</comment></comment></comment><comment><USER23> Relevant anecdote: For a high school ICT project my class had to make an educational game in Visual Basic. I made a 'math invaders' clone where you answer simple algebra sums (e.g. 5 + x = 12) to defeat the relentless hordes of aliens. At home my 8yo brother watched me play for about 5 minutes, then exclaimed 'Oh I get it, the letters are like numbers that you have to find!', then went on to play the game himself for hours. He learnt algebra about 6 years before any of his classmates through gamification, and years down the track enjoys math more than many of his friends.

</comment><comment><USER24> This looks extremely interesting, I have a 5 year old daughter that I want to see the playful side of mathematics before she hits the typical US Maths curriculum. One of my guiding documents has been "Lockhart's Lament" [1], but trying to figure out how to make that a reality for her has been difficult for someone like me with so little time! I am going to check this out tonight!

[1] [http://en.wikipedia.org/wiki/A_Mathematician%27s_Lament](http://en.wikipedia.org/wiki/A_Mathematician%27s_Lament)

</comment><comment><USER25> If you're interested in this kind of work, and especially if you're also interested in using computers to open up new kinds of mathematical play and learning, you should read Seymour Papert's "Mindstorms" book.

The ideas are powerful and radical. Radical enough to explain why run-of-the- mill schools never successfully integrated awesome tools like LOGO and its descendants. They can't deal with learning that's so child-driven and free.

</comment><comment><USER26> There was a study done in a place quite unexpected to me now, and interesting back then when I was in school myself.

My Math Teacher told there were some schools where a pilot was conducted teaching calculus concepts from 5th,6th std students and were monitored till they did their graduations and career paths.

Interestingly the people who were chosen randomly, performed equally well and their decisions in addition to math were more logical.

This study was done in India :)

</comment><comment><USER27> "Revolutionizing the way math is taught" and not "memorizing multiplication tables as individual facts rather than patterns" sound like very worthy and important goals. At the same time, it's hard to judge this particular initiative based on the article; it might be Hippie Math for Rich Kids Who Will Study Humanities Subjects and Become Trustafarians by a Berkelely Yoga Instructor"

</comment><comment><USER28> > _But they also need to see meaningful (to them) people doing meaningful > things with math and enjoying the experience._

I was wondering if this was essential for the learning process of five or six year olds.

Making maths enjoyable for young children would be the primary concern, but showing something meaningful (not necessarily to them) being done with maths by someone meaningful (to them)? It would work better if:

 _The kids require to see something that is relevant to_ their _interests or needs being solved with maths by any old codger, as long as said codger can adequately manipulate algebra._

By the way, who is going to teach these children algebra? A fair number of teachers won't be up to the task. Reminds me of the _learn to code_ buzz- phrase being passed around - first off you need to spend money and time on teaching teachers how to code.

EDIT: bloomin' asterisks.

</comment><comment><USER29> [http://siterecruit.comscore.com/sr/atlantic/broker.js](http://siterecruit.comscore.com/sr/atlantic/broker.js) is holding up the entire site for me. Async, anyone?

</comment><comment><USER30>
      "What is learned without play is qualitatively different. It helps
       with test taking and mundane exercises, but it does nothing for
       logical thinking and problem solving. These things are separate,
       and you can't get here from there."

This is the core of what people mean when they — legitimately — talk about 'passion'. Did you learn computing (or any field) for fun, or alternatively because you thought it paid well, or your parents wanted you to do it, or whatever.

(Not to be confused with 'passion' as mbaspeak for 'naïvité enough to work ridiculous hours for peanuts'.)

</comment><comment><USER31> Maria co-authored a great book aimed at making higher level math concepts fun for schoolchildren titled Moebius Noodles. The site appears to be down now, but here's the FB page: [https://www.facebook.com/moebiusnoodles](https://www.facebook.com/moebiusnoodles)

I highly recommend it, as well as signing up to receive periodic emails from Yelena/Maria with additional activities, tips and information.

</comment><comment><USER32> Obligatory Star Trek reference: [http://www.youtube.com/watch?v=ETt8GJRbqLc](http://www.youtube.com/watch?v=ETt8GJRbqLc)

</comment><comment><USER33> I've thought for a long time that an abstract approach might work better than a concrete approach for introducing children to math.

I remember when my kids were in kindergarten, and their math education started with _estimation_. My first thought was, "Great. Now they've turned _math_ into a touchy-feely all-answers-are-right-answers nonsense subject!"

<comment><USER34> I don't want to turn math into a touchy-feely all-answers-are-right-answers nonsense subject, but estimation is a good skill in math, engineering, and computing.

Two examples: Fermi problems[1] and Jon Bentley's "back of the envelope"[2] estimates.

[1] [http://en.wikipedia.org/wiki/Fermi_problem](http://en.wikipedia.org/wiki/Fermi_problem) [2] [http://www.csie.fju.edu.tw/~yeh/research/papers/os- reading-l...](http://www.csie.fju.edu.tw/~yeh/research/papers/os-reading- list/bentley-cacm84-envelope.pdf) and [http://www.eecs.harvard.edu/cs261/background/p176-bentley.pd...](http://www.eecs.harvard.edu/cs261/background/p176-bentley.pdf)

<comment><USER33> I agree that estimation is important. But so important that we start children with it? That smells wrong to me. Estimation is about intuitive thinking. Mathematics is usually a child's first introduction to formal, rigorous thought. Don't go soft on it.

</comment></comment></comment><comment><USER35> I definitely appreciate that math is much more than numbers and equations...

On the other hand teaching a kid math has to at some level at some point revolve around taking some numbers and getting other numbers out...

I cant really see how one can do algebra without knowing arithematic. algebra is fundamentally a different beast but you just cant do it without some kinda arithmatic

<comment><USER36> > On the other hand teaching a kid math has to at some level at some point > revolve around taking some numbers and getting other numbers out...

Yes, but perhaps not the very first thing. To me, the first thing should be interesting, aesthetically pleasing patterns -- images -- that have mathematical meaning ([http://arachnoid.com/mandelbrot_set/graphics/title_image.jpg](http://arachnoid.com/mandelbrot_set/graphics/title_image.jpg)). Then, when the student's curiosity has been aroused, we can "open the machine" and show its inner workings.

> I cant really see how one can do algebra without knowing arithematic.

But that's easy. I'm not necessarily recommending it, but one can easily have algebra without numbers. Remember that the most useful algebraic equations are those in which the numerical values are irrelevant.

</comment></comment><comment><USER37> Ever since I took Discrete Math in College, I have thought it would be a great way to introduce school kids to Math.

</comment><comment><USER38> Does anyone else find math like trig and calculus dramatically easier to comprehend than stuff like combinatorics?

<comment><USER13> Combinatorics has always been easier to comprehend for me, but the problems have always been harder. That's because calculus depends on higher-level concepts but is otherwise rote, whereas combinatorics depends on only the most elementary concepts but the problems quickly become very complex. I think this is why combinatorics features so much more strongly in math competitions than does calculus.

</comment></comment><comment><USER39> Am I the only one that enjoyed math more earlier than now? I loved calculus and geometry in high school and undergrad, but now in graduate school I can't follow the physicists at all, and my eyes just glaze over.</comment>


YC Startup School: Build Sprint and Equity-Free Grants - <AUTHOR> https://blog.ycombinator.com/announcing-yc-build-sprint-and-20-equity-free-grants/ <comment><USER2> I started Startup School about 7 months ago and went from side-project to a full-time cofounder [1]. I (23M) am a first-time technical entrepreneur, and I cannot emphasize enough how beneficial YC's resources are for those who just start.

The most important thing which is told to you over and over again while you are doing Startup School is "talk to your users (potential users)". Talk to them before writing the first damn line of code. Only after you have 20-100 people who told you "yes, that is my problem which must be resolved" start working on your solution to this particular problem.

Still, about 80% of people who I met over SS weekly sessions completely neglected those rules. They were building to build not to solve the problem.

Also, AWS credits saved us thousands of $. I did not know about these credits until I randomly clicked on a "deals" tab of SS interface.

This "Build Sprint" is truly a great idea that will finally highlight the success of those teams who listened to YC's advises.

Finally, I think because of SS is free many people do not value their advises. However, SS literally has 99% of what you need to know to build a 100k-1M ARR business. That's why I think SS should be somewhat paid/exclusive to make people value it.

[1] [https://newscatcherapi.com/](https://newscatcherapi.com/)

<comment><USER3> _Only after you have 20-100 people who told you "yes, that is my problem which must be resolved" start working on your solution to this particular problem._

This is good advice if you want to 'do a startup', and maybe that's the sort of person startup school attracts, but it seems incongruous with the majority of founders I know who started by solving a problem they had themselves. They built something because they needed it to exist, and a business grew out from that.

Building to distract yourself from more important work on your startup (eg testing your assumptions) is a bad idea but building because you actually need the thing to exist isn't.

<comment><USER4> I need a thing to exist (calorie counter), but I also talked (if only superficially) to other people like me about the issue. I still got a lot of insight out of that. You wouldn't expect the number of tiny, innocent assumptions you make that hold for yourself but are utterly not the case for others.

For example, the fact that I live with my partner and many of my potential users don't means they can apply a fundamentally different process to tracking calories than me. You are not going to realize stuff like that on your own.

So even if you're mostly just fixing your own problem, just talking to a few people and making minor changes accordingly can make your product useful for a way bigger audience. Or maybe better stated conversely, not talking to others will narrow your products' audience down immensely.

<comment><USER2> Same, we fixed our own problem. Still, talked to others to understand if there is a demand. Because there is always a chance that it is only you who have such issues.

</comment></comment></comment></comment><comment><USER5> Hey HN! Really excited to launch the YC Build Sprint. We've been working on this for the last month. The main goal here is to help founders get as much done as possible in a 4-week period. We've found that time pressure can be really helpful for productivity, even if it's external (and even somewhat contrived).

<comment><USER6> Thanks kcorbitt! Apologies if this is not the place to report this but invited co-founders get an 'Invite not found!' error after clicking on the invite link in the email and after filling out the profile.

<comment><USER7> Could you email email@example.com? We can help out!

</comment></comment></comment><comment><USER8> In my opinion, Startup School is kind of a waste of time.

If you have the capacity and the will to build for yourself, you should already have the drive to push your idea forward. You don't need validation from them to make it work.

I hate getting judged by a "panel of experts" and their "opinions" destroying the wills to continue. Self-confidence and constant iterative validation are a big part of the founder's success. YC's model of "only the top 1% gets funding and support" has stopped producing unicorns. It exerts bias and provides false validation to the founders leading them into a false sense of security.

Resources are great, but I wouldn't waste time on a program like this. Especially they pick only 20.

<comment><USER9> I am a founder who has been trying for many years. I have a set of mental issues including insecurity (which is way better now) and I totally depend on peer group of founders to help me along.

Just for reference, last 2-3 weeks were a complete blank. I spoke to a few founders for motivation but I could not drive work.

If you have the capacity to work without any support, good for you. I am not in these networks for YC validation though. I am there for the peers, they help immensely. In fact I want to create an alternate place for founders, but many already exist and I am a part (PH, IH, Makerlog) of them too.

<comment><USER10> Where is the community in PH? Also everything that is top ranked on PH has a majority of vague or empty positivity. Being positive is good, but not the way PH and Yourstack are.

<comment><USER9> PH Makers, it is not as matured a community but it is getting there. I am not talking about PH ranking (homepage).

<comment><USER10> Ah okay. So the wip.chat and makerlog clone? Based on principles. I don't know. Don't feel right using the bigger corp copying product.

</comment></comment></comment></comment></comment><comment><USER11> YC needs a version (or sub-section) of startup school that's focused on generating quality startup ideas. I feel like that's a huge aspect that isn't really talked about. This "Build Sprint" is an example...they jump right to "let's figure out how to get your first customers", and assume everyone is ready to go with a million-dollar idea.

<comment> grey-area There are no million dollar ideas.

There are only difficult decade-long slogs through the hard work of building a company, which may or may not one day yield a million dollars.

Take spacex for example, which started like this and 20 years later is aiming for Mars

[https://www.starletters.com/wp- content/uploads/2017/12/maria...](https://www.starletters.com/wp- content/uploads/2017/12/mariachi.png)

Or Amazon, which started like this and took a long long time to become one of the biggest companies in the world

[https://www.reddit.com/r/pics/comments/7p9n1j/photo_of_jeff_...](https://www.reddit.com/r/pics/comments/7p9n1j/photo_of_jeff_bezos_in_1999_think_about_this_the/)

But most people don't want to do the work so they look for million dollar ideas.

<comment><USER11> I'm not discounting moonshot business ideas. I'm saying there's a bunch of capable people out there that may not have any idea what exactly to build. And I'm saying people like that could benefit from active discussion on ideas of what to build, and people that already have ideas of what to build would benefit from discussing their startup idea & business plan with others prior to diving in head first.

I'm basically saying mix wisdom of the crowd with the startup-idea generation process.

<comment> grey-area Quite sincerely, I'm convinced YC and other VCs don't do this because they've observed that ideas truly don't matter very much. And if you can't even come up with an idea what hope do you have of finishing the work, why not become an employee (which is fine)?

What matters is the journey and how you react to the multiple problems along the way (99% of people give up too early, too much grit is required). Usually by the end of that journey your initial idea has changed beyond recognition, even if there are some common elements between the idea and the endpoint.

To come up with some examples:

Apple: Computers for everyone -> Phones for everyone

Amazon: Buy books online -> Logistics, Free Delivery + Cloud Compute

Airbnb: Airbeds in living rooms -> Online bookings

SpaceX: Greenhouse on Mars -> Reusable rockets

Very few ideas survive contact with reality unscathed.

<comment><USER12> if ideas don't matter, explain Uber and the dozens of copy cat apps that launched right after all over the world. Why didn't they launch before Uber was even thought of by the founder?

</comment></comment></comment></comment></comment><comment><USER13> Really cool idea! I'm working on a project that could really, really use 4 weeks of focused effort, and I think that's enough time to accomplish a lot but short enough it doesn't feel overwhelming to zone in on it for that long. Looking forward to be a part of it!

<comment><USER14> I'm in the same boat, this looks exciting!

</comment></comment><comment><USER6> I'm not very familiar with Startup School, can students who participated recently chime in about the amount of value obtained and time commitment involved? Is it possible to complete outside of PST business hours or are there real-time components? Thanks!

<comment><USER15> I try to participate in Startup School each time it comes around. I find it incredibly good practice for "the real thing".

I'm not quite ready to start my own venture just yet, but I like to "practice" by coming up with an idea, setting goals, moving towards them, doing interviews, etc. The startup school is a really nice program to follow along with and have conversations with other founders during. I'm basically using it to war-game a startup launch myself. The idea being that when the time comes that I decide to jump in on something I'm very passionate about and put skin- in-the-game, it should all feel familiar (if not just a tiny bit more comfortable).

Of course it's not a substitute for the real thing, but I think it's brought immense value to my skillset.

</comment></comment><comment><USER16> I'm kind of at a loss for what they expect the "sprint goals" to be.

Would people who've been through this program be willing to share what their sprint goal was along with how mature their project was, what kind of experience they had and whether they achieved their sprint goal?

<comment><USER17> While the selection criteria seems pretty subjective, if you want a chance at winning the $10K grant then your work should focus on business growth. They mention examples like launching V1, but the criteria has no real focus on product progress or technical achievements.

In fact, it seems like simply running a successful marketing campaign for your preexisting product would set you up for success in this "sprint".

More specifically, the selection criteria reads:

A panel of qualified judges determined by Sponsor (YC) in its sole discretion will select as the Winners the Participants with the twenty highest-scoring Submissions from among all eligible Submissions received by the Submission Deadline based on the following criteria:

* Participant's revenue or prospects for revenue in the near term (25%)

* Participant's business growth as measured by an increase in users, increase in revenues, progress in bookings or improvement in the Participant's objectives ("Business Growth") (25%)

* Scalability of Participant's business (25%)

* Feasibility of implementing Participant's proposed business objectives (25%)

Source: [https://docs.google.com/document/u/0/d/1YSvivbXQGTH8bHLTfIwj...](https://docs.google.com/document/u/0/d/1YSvivbXQGTH8bHLTfIwjzNwkUGcwZfuXZJrsL2EFF2k/mobilebasic)

</comment></comment><comment> 100-xyz I have registered for this, set a goal of 150 registered users and 2 paying users and then panicked. Here is the relevant blog [https://toonclip.com/blog](https://toonclip.com/blog)

</comment><comment><USER18> Does anyone know how frequently these are offered?

<comment><USER19> IMHO, YC tends to launch these kinds of programs around summer.

The first iteration of this was launched in July 2015 and it was called the YC Fellowship. Participation was accomplished remotely via video chat and grant money was $12000.

[https://blog.ycombinator.com/yc-fellowship/](https://blog.ycombinator.com/yc- fellowship/)</comment></comment>


What Cyber-War Will Look Like - <AUTHOR> http://scholars-stage.blogspot.com/2018/07/what-cyber-war-will-look-like.html <comment><USER2> IMO if you want to know what cyber war in the immediate future will look like read up on the Ukraine in recent years.

Trying to sow confusion via bank fraud, online harassment and propaganda like described in the article only works until people realize what's going on and make it known. It would certainly work well to some extent but once people realize what's going on it's all #fakenews. If you try to commit bank fraud en-mass banks will catch on and start ignoring you. If you try to slander leaders en-mass people catch on and start ignoring you.

</comment><comment><USER3> Who needs any of that? Just remove people from the voter registration of candidates that disapprove of you in their country.

Oh that already happened?</comment>


Designing Layouts with CSS Gridbox - <AUTHOR> https://blog.gyenabubakar.dev/designing-layouts-with-css-gridbox-ckd57mb8p00eq5ys14cd80c8z <comment><AUTHOR> One of the best articles on CSS gridbox, I have read recently.</comment>


Everybody is racing to an IPO – even Laird Hamilton's young "superfood" company - <AUTHOR> https://techcrunch.com/2020/08/31/everybody-is-racing-to-ipo-even-laird-hamiltons-young-superfood-company/ <comment><USER2> Yes. Everyone and their cheetah's and probably the whole animal kingdom are racing for a IPO exit scam before the big flood happens; i.e. market crashes.

Just avoid buying stock at the IPO prices of companies that continuously are racing into the red rather than into profitability and sustainability.

</comment><comment><USER3> This one is pretty ridiculous. They lost 9M last year, don't have a unique product. Mixing coconut powder and sugar doesn't make anything special. Sounds like a last ditch attempt to get some production going. Curious to see gross and net margins</comment>


StraightToThePoint, yet another web-based presentation tool - <AUTHOR> http://info.iet.unipi.it/~luigi/sttp/

<comment><AUTHOR> this is yet another web-based presentation tool. Compared to other similar tools, the two major advantages are: i) a simplified syntax for slides, similar to reStructuredText <http://en.wikipedia.org/wiki/ReStructuredText>, and ii) a simple server-side backend so that multiple "listener" can have their slides move in sync with those of the speaker. Resizing using the browser's controls (ctrl +/-) generally works well to adapt to different screen resolutions, and i am trying to add support for tablets and phones and similar devices. There is also a simple "edit" mode in which you can modify, still within the browser, the textarea that contains the presentation, and rudimentary support for plotting, and some simple transition effects.

sttp shares the disadvantages of this family of solutions: if you have images or other embedded content the presentation is not a standalone file; export- to-pdf is weak; no math; etc. - but it can do the job for small presentations, and especially it really enforces you to have a consistent slide style across the presentation</comment>


A basic usability test on ten phones - <AUTHOR> http://www.quirksmode.org/blog/archives/2010/01/a_basic_usabili.html

<comment><USER2> I have been an iPhone user since whenever the first one came out. I now own an iPhone 3GS. I recently (3 weeks ago) bought and tried my very first android phone (with OS 1.6)

I have really never been so disappointed in my life. This thing is supposed to compete the iPhone? The movement is not smooth, the interface flickers, buttons don't react immediately, the keyboard is laggy and the entire thing feels so unpolished.

I instantly hated it. I still have it - I use it for development, but Android 1.6 is not even close to the iPhone in 'goodness'. Maybe 2.0 will be better.

On the other hand, I wrote my first program for it. Programming for Android is MUCH easier, a lot more intuitive and there are so many widgets that you can very quickly get things sown together. Android programming reminds me of programming in Basic, while iPhone programming is like normal C++ programming.

I know java somewhat and C++ very well, and it took me like a month to really feel I understood iPhone programming. It took me 2 or 3 days to feel comfortable programming for Android.

I have not yet sold anything on the Android market, but when I do I'll be sure to post a comparison of the two platforms with the exact same app. In a week or two I will have my first Android app up.

<comment><USER3> SO, you are actually saying the hardware you have is crap. I guess with the newer phones (nexus one, xperia x10) the UI will be as responsive as you know it from your iphone and android will begin to shine.

<comment><USER4> Smoothness of UI is as much about software as it's about hardware. My Macbook Pro is a super-powered work horse compared to iPhone, but still many applications and web pages do not give a great smooth, experience.

Reason? Because asynchronous, multithreaded programming, which is required for smoothness, ain't trivial with abstractions that current programming languages and platform libraries provide.

<comment><USER5> With any hardware made in the past couple decades, it's _entirely_ about software. Plus, asynchronous, multithreaded programming isn't required for a perfectly smooth interfaces.

Consider the enormous amount of _instantly_ responsive software on 1 to 4mhz 6502s (Atari 2600, NES, C64, Apple II, Atari 8-bits, etc).. Every current platform, even the phones, can emulate those at multiple times real-time speed, so the hardware is certainly capable of it.

In the 2600s case, it didn't even have video memory and a video chip to help the CPU. The programs had to be timed to output straight to the TV at the exact speed and time the TV needed data. No threads or asynchronous events to help there.

</comment></comment></comment></comment><comment><USER6> Nice read, but the writer uses the phrase "sends this Obigo browser through GWT hell". Unless Google is doing more complex user agent sniffing that I thought, the phone's browser not being able to use Javascript is just that, the phone browser's problem, and not Google's fault.

A more basic test I'd like to see is how well do these 10 phones stack up wrt to the task at hand. AS PHONES.

I have a smart phone, and my biggest annoyance? The simple task of "I have a phone number and I need to call it" is far more complex than it needs to be. Calling contacts already in the phonebook? Easy. Punching in a phone number has far too many buttons to get back main screen, go to phone mode and bring up the actual dialer. Once there, either it's a touchscreen without real buttons, or it's a sub-qwerty tiny keypad that may as well be annoying touchscreen at that size (The kind that RIM is quite fond of). (Connection services like Google Voice are up to the should-be-trivial task though).

Then again, I suppose the smartphone route would be to print up QR codes on everything and allow dialing of a cellphone camera picture.

<comment><USER7> This is where I believe the iPhone wins at the moment.

It works brilliantly, for me, as a phone. I've not found another smart phone as good so far.

<comment><USER8> The path from locked state to dial is quick enough for me on a 3GS, but I have to admit it's probably more steps than I would like. On paper, it actually looks kind of bad if it's a number you don't have in-directory:

1\. Hit home or lock key 2\. Swipe lock slider 3\. Touch phone icon 4\. Touch dialpad icon 5\. Dial number

Vs. a featurephone or keyboarded smartphone

1\. Hit unlock key or open clamshell 2\. Dial number

What I'd actually like to see is a second slider on the iPhone's lock screen that goes straight to the phone without stopping by the springboard. That would pretty much bring it to parity with featurephone keypads.

<comment><USER9> second slider is brilliant.

<comment><USER9> it wouldn't even be unintuitive. longways slide (current) for regular home. sideways slide to go straight to phone. I can't believe no one has thought of this.

<comment><USER10> Nexus One uses a two-way slider to answer calls -- left-to-right to answer, right-to-left to send to voice mail.

I found it terrible. Unintuitive, and hard to use even when you understand what it's doing.

<comment><USER9> yeah, but don't you think it would be better if they were in totally different axes?

</comment></comment></comment></comment></comment></comment></comment><comment><USER11> Do people really like styluses that much? I guess they're good for tapping very tiny screen elements, but zoom pretty much solves that.

I wonder if B's opinion would have changed had he spent a few hours with each phone trying to do some other tasks.

<comment><USER12> I am writing this standing here, waiting for the train. It is couple degrees below zero. Stylus alllows me to keep my gloves on - I see that as a HUGE bonus.

<comment><AUTHOR> North Face's E-Tip gloves let you use capacitative touch screens while your fingers are toasty warm.

<comment><USER13> You can add this feature to other gloves with a few inches of conductive thread.

[http://lifehacker.com/5412625/make-any-pair-of-gloves- work-w...](http://lifehacker.com/5412625/make-any-pair-of-gloves-work-with-a- touchscreen)

</comment></comment></comment></comment><comment><USER14> Shame he didn't try an Android with a hardware qwerty keyboard. I've got a G1 Dream Dev, everyone that's tried it has liked it. It has a very nice tactile feel. I tried a few handsets and nearly bought an E71, luckily it couldn't get a decent bundle for it.

I was looking forward to the Google phone but sw kb is a turn off.

The G1 does have its downpoints - the scroll wheel jumps from link to link which means more thumb movement if you need to scroll with the screen. And the battery life. Oh that's the killer, great if you're not using it but spend an evening doing a bit of browsing and showing people youtube vids when you wake up in the morning you can't call a cab. Carrying a mini usb cable is required.</comment>


Scientists have discovered a warm-blooded fish - <AUTHOR> http://www.washingtonpost.com/news/energy-environment/wp/2015/05/14/scientists-have-discovered-the-first-warm-blooded-fish/

<comment><USER2> This fish is not "fully warm-blooded". As described in the article, it does not target a specific body temperature like mammals or birds. It just uses its muscles to warm itself, like some species of snake and insect do.

<comment><USER3> Does targeting a specific temperature determine if you're classed as warm blooded?

Relevant article snippet:

"Some other types of fish, such as tuna, have similarly designed blood vessels in certain parts of their bodies, allowing for "regional endothermy" — warm- bloodedness that's limited to certain organs or muscles, such as the eyes, liver or swimming muscles.

But the opah is the only fish scientists know of that has this design in its gills, where most fish lose the majority of their body heat to the surrounding cold water. By warming up the blood in the gills before it goes anywhere else, the opah achieves not just regional endothermy, but whole-body endothermy, according to the paper's authors.

Testing showed that the opah is able to maintain a core body temperature about 5 degrees Celsius warmer than the surrounding water."

<comment><USER4> The nice thing about warm-blooded animals targeting a narrow body temperature range is that our genetic and protein structures can be much simpler.

A cold blooded animal has to have a wide selection of proteins to do the same job at different temperatures. A warm blooded animal needs just one.

<comment><USER5> Air cooled Volkswagen tolerances.

</comment></comment></comment></comment><comment><USER6> meh, this seems to be equivocation. basically, warm blooded (and cold-blooded) are no longer used (because they found animals didn't cleanly fit into the features of each), so they have a bunch of other words that describe the components of blooded-ness -- like, does the animal maintain a specific body temperature, does it use heat to convert sugars into (ATM) energy. What they've found is the first fish to warm water on entry to gills so that THAT water doesn't bring the temperature of the fishes body down too low.

meh

<comment><USER7> Basically yes, though according to the article the fish is heating cold blood with warm blood, not the water passing through its gills.

Like birds legs: [http://askanaturalist.com/why-don't-ducks'-feet- freeze/](http://askanaturalist.com/why-don't-ducks'-feet-freeze/)</comment></comment>


Ask HN: CLI tool to download webpages and convert to Markdown? - <AUTHOR> Is there a CLI tool that downloads webpages and converts them to Markdown?<p>I've just started using Obsidian https://obsidian.md/ and would like a way to save interesting blog posts and articles. <comment><USER2>
      curl --silent https://example.com/foo.html | pandoc --from html --to markdown_strict -o foo.md

From _Converting HTML to Markdown using Pandoc_ [http://www.cantoni.org/2019/01/27/converting-html- markdown-u...](http://www.cantoni.org/2019/01/27/converting-html-markdown- using-pandoc)

<comment><USER3> I tried that on a HackerNews page and the content of the output file foo.md was in html.

<comment><USER2> Sorry, had only tested it on my own site, which worked as expected:

      curl --silent https://tinyapps.org/ | pandoc --from html --to markdown_strict -o index.md

</comment></comment></comment><comment><USER4> I find Joplin [https://joplinapp.org](https://joplinapp.org) does a good job of producing markdown from web pages and already has sync capability built in. Looks like it would be ideal for working with Obsidian

<comment><USER4> Exported my Joplin markdown and opened it up in Obsidian. Works like a dream and the best part is Jopli already has it's own web clipper. Seems like a superb match

</comment></comment><comment><USER5> I made this a couple weeks ago: [https://www.npmjs.com/package/@dougskinner/markdowner](https://www.npmjs.com/package/@dougskinner/markdowner)

</comment><comment><USER6> [https://github.com/aaronsw/html2text](https://github.com/aaronsw/html2text)

<comment><USER2> Thank you, Anand. Despite being 8 years old, Aaron's html2text.py worked perfectly to convert the HN homepage to Markdown. His memory (and code) continues to be a blessing!</comment></comment>


History Repeats - Facebook is the new AOL - <AUTHOR> http://www.convinceandconvert.com/facebook/history-repeats-facebook-is-the-new-aol/ <comment><USER2> And in 5 years time, it's very possible that Facebook, like AOL, will be dominated by old people, the stubborn, and the relatively computer illiterate, as others have moved on to greener pastures.

Facebook's dominance is not set in stone. People may not be able to live without Facebook, but there's no reason they can't transition, such as how people quickly transitioned away from MySpace.

You start by having two accounts. The more interesting, cutting edge, friends are on the new network. Your high school friends, family, and tertiary relationships are on the old network. You check them both equally at first, but slowly you find yourself on the new network more often. Then, at some point, you stop updating the old one, save for the occasional "I don't use this anymore, I'm on X now." updates. Others follow suit, until at some point, the trickle becomes a flood. Next thing you know, the old network is a ghost town. Nobody cares about it anymore, and people only reference it as a relic from a distant past.

There is nothing Facebook has done to prevent this. And this will keep happening until social networking is eventually decentralized.

<comment><USER3> That's interesting, actually. I think Facebook Connect might be the start of preventing that from happening.

Say, for instance, they chose to become more platform-oriented, providing the data/services of facebook to developers. Suddenly, developers could build on top of an fb-platform allowing users to update from one central location. They could provide specific services (wall or no wall) and extend services (which would be specific to that site...)

"Have a facebook connect account? Sign in today to expand your profile page on the-latest-greatest.xyz!"

All your friends are still "friends" and communication is still possible, regardless of where on the web your social networking "home" resides.

</comment></comment><comment><USER4> The idea is not new ("Facebook is the new AOL") - it's been said many times here. BUT, I did find one slide to be really interesting: "Imagine if before you searched, Google asked you this..."

</comment><comment><USER5> Anyone remember Googlezon ? That EPIC2014 project which was talking about how the world was going to be taken over by a merger of Google and Amazon. When I joined Google in 2006 there was joke about putting into the new hire orientation that you didn't need to forward the video to the misc list :-)

That didn't mention Facebook at all, most people thought MySpace was going to dominate social. Anyway, ...

People who had been around computers and networking have known since their first (or maybe second) class on data structures that structured data _was_ computation. The last node in an LRU list _is_ , because of the structure, computed to be the oldest node in the list. One of the really cool things about Python was list comprehensions is "foo" in bar?

So its sort of a yawn when we see that you can infer a traffic jam by the smart phones sending in position data periodically, or that the movie 'companion' suggestions from Amazon are all from genres you've previously purchased. But its just dawning on a lot of folks.

This blogger thinks Facebook is AOL because they have grown rapidly and have a valuation they don't understand and a number of page views that made their AdSense ID salivate. They equate AOL's walled garden to a castle. They draw a parallel between Facebook's other properties and the kind of walled garden that AOL once supported.

And yet they miss evidence that Facebook isn't a service that people use, it is people instantiating themselves in what is most like a network directory service. Humans as nodes in a n-tree of relationships and desires (likes) and even dislikes.

Peter Warden's original "who your friends are hack" illustrated so clearly, you don't have to 'guess' you can _know_ truths by looking at the data structure that is Facebook. This is not something AOL even imagined.

</comment><comment><USER6> Just for reference, here is John C. Dvorak's 2010 article of pretty much the same title: <http://www.pcmag.com/article2/0,2817,2372729,00.asp>

</comment><comment><USER7> So we'll know this cycle has peaked when Facebook buys Time-Warner.

<comment><USER3> Or, everyone leaves facebook for a more "true" social experience. How about social networks created dynamically based on your location with the people around you? You know, real life social interactions. (Color, for example?)

Left are parents (and grandparents) who update their statuses and post on walls because they're comfortable with facebook and don't really understand that "other" stuff...</comment></comment>


iPhone App Digitizes Sheet Music, Teaches You Piano - <AUTHOR> http://www.wired.com/gadgetlab/2010/03/etude-iphone-app/

<comment><USER3> Huge congrats on the app... with the iPad coming out, it's the perfect time for this.

A possible area for expansion (or maybe even a new app entirely). There's a whole world of classical music that is extremely competitive. Since you've got the iPad sitting on their piano, use the microphone to record yourself playing the song, and then it can be uploaded automatically and rated alongside others who've played the song.

Then you can have a leaderboard for each song, and even an overall leaderboard, like a global tennis rankings. They could challenge each other to a "duel" like a tennis match, or there could be a tournament. People can have their ranking, a profile, how old they are.

It would be hugely motivating to kids learning to play, and very disruptive/democratizing to the whole classical music world.

<comment><USER4> Guitar Hero against other people online with real instruments could be an epic music education tool.

<comment><USER5> That's what Jesse Schell talks about in his great talk at Dice.

[http://fury.com/2010/02/jesse-shells-mindblowing-talk-on- the...](http://fury.com/2010/02/jesse-shells-mindblowing-talk-on-the-future- of-games-dice-2010/)

</comment></comment></comment><comment><USER6> Congratulations Dan. Looks like you have created a useful, highly polished little app. I'd buy it if I had an iPhone.

Have you considered making the keys on the keyboard start off a lighter shade of blue and fade down to dark blue as they are held?

</comment><comment><USER7> Currently 6 months into learning the piano again, downloaded the app to give it a whirl.

Very first impression, but the Continuous scrolling seems to be a little jerky in places.

Edit: it's synching up with the notes as they scroll by which is your design choice I guess. Smooth continuous scrolling wasn't something that seemed appropriate?

<comment><USER7> After listening to the following TED talk, I feel that your store could do with some Chopin.

[http://www.ted.com/talks/benjamin_zander_on_music_and_passio...](http://www.ted.com/talks/benjamin_zander_on_music_and_passion.html)

<comment><AUTHOR> There was a last-minute problem with the 2 Chopin songs that were ready to go live with the app. Hopefully have em next week.

<comment><USER7> Another comment: when playing through For Elise, it plows right through the 1 and 2 endings for each section when it should play the 1 ending before doubling back and playing through again before playing the 2 ending.

</comment></comment></comment></comment><comment><USER8> The UI looks good, but I have a hard time imagining it in use. Isn't the iPhone screen tiny for this purpose? Why not make a general laptop app or web app?

<comment><AUTHOR> Because I don't think Wired would cover it if it were a desktop/web app :)

<comment><USER9> Dan, was it your post on HN that got you on wired.com? Or how did that work?

<comment><AUTHOR> No, unrelated.

</comment></comment></comment></comment><comment><USER10> I wouldn't have thought of sheet music as a killer app for the iPad, but now that I think about it, that makes perfect sense. Anyone working on iPad stands for instrumentalists yet?

I'm picturing entire orchestras switching from sheet music to digital displays. The article mentions the portability and findability benefits of replacing stacks of paper with a single screen synced to a sheet music library. jgilliam posted here about the potential benefits of building games on top of sheet music. But just in terms of simple usability for instrumentalists, imagine sheet music that automatically flips to the next page at the right time.

</comment><comment><USER11> When I was in elementary school (even though I have not developed any musical talent), my favorite part of music class was when the teacher (who was a talented pianist) would sit down and play at his then-state-of-the-art keyboard towards the end of class. His actual notes would show up on a huge keyboard display where keys would light up, just like in your app. It was fascinating and mesmerizing to see the visual patterns of some songs - <USER2> that some complex songs weren't that complex.

Thanks for the beautiful app and memory trip.

<comment><USER12> When I was younger I played a cello solo of Cavalleria Rusticana Intermezzo. It was almost 4 minutes in length and filled, at most, half a music sheet (~8 bars). Graphically the music wasn't complex, but it was all the little details (soft, loud, fast, slow, extremely long holds) that made it interesting. Just looking at it you wouldn't be able to make sense of it. Only through playing it would the timing and pattern emerge.

</comment></comment><comment><USER13> I'm sure you've already thought of this, but it seems like now that you have input of OCR sheet music, you should strongly consider output of OCR sheet music.

Allow your player to set the metronome, then capture what they play on Etude. Output a sheet music transcript that they can tweak, replay, and publish in a marketplace of free music. People can transcribe public domain music, share original compositions, or (tricky part maybe) cover licensed music.

</comment><comment><USER14> It looks like a nice app but does it actually do anything that is different from the multitude of desktop apps in this genre?

<comment><USER15> Primarily, it doesn't require a desktop - useful if you're sitting at a piano.

It's also a very polished app with a convenient in-app sheet music store.

<comment><USER14> > Primarily, it doesn't require a desktop - useful if you're sitting at a > piano.

Yes I had worked that part out. My question wasn't intended as criticism. The context it appeared in lead me to believe there was something else new about this but I couldn't find it so I asked. I have an interested in this area. By the looks of things this would be particularly good with a larger screen such as the ipad.

</comment></comment></comment><comment><USER16> Great idea, poor hardware choice.

Really - this would be an amazing app for an aspiring musician but the iPhone screen would make this experience much less enjoyable than it should be.

<comment><USER17> I think that's where the ipad would do a better job at simulating full sheet music. I suspect the developer has this in mind already.

</comment></comment><comment><USER18> You're in the money!

</comment><comment><USER19> wired wrong again, if it's using midi I'm pretty sure the application doesn't digitizes anything.

<comment><USER20> It's digital _sheet_ music, not audio.

<comment><USER21> The point still stands, though: the app doesn't digitize the sheet music, it displays it from sources that have already digitized it.

Unless the scores are beying keyed in by hand, the actual digitization of the sheet music is basically a specialized OCR: <http://en.wikipedia.org/wiki/Music_OCR>

<comment><USER22> Doesn't it mean it digitizes the "process" of sheet music -- the whole thing from notes to someone playing it? Not just the sheets with the notes on them. This meaning for "the app digitizes sheet music" makes sense, at least for me.

</comment></comment></comment></comment><comment><USER23> Big congratulations to Dan. Excellent app. I like it when people deliver real apps.

</comment><comment><USER24> Fuckin baller!

</comment><comment><USER25> Kudos.</comment>


User Experience Videos - <AUTHOR> http://www.smashingmagazine.com/2010/01/05/25-user-experience-videos-that-are-worth-your-time/

<comment><USER2> I'd add Ryan Singer's "UI Fundamentals for Programmers" (<http://windycityrails.org/videos#4>) to the list also. He did a really great job of explaining how to think about design and some simple rules to follow.</comment>


NASA advisory committee questions SpaceX's unorthodox fueling process - <AUTHOR> http://www.wsj.com/articles/nasa-advisory-group-raises-concerns-about-spacex-rocket-fueling-plans-1477955860 <comment><AUTHOR> Paywalled; content similar to this LA Times story, which cites WSJ, and is free:

[http://www.latimes.com/business/la-fi-spacex- nasa-20161101-s...](http://www.latimes.com/business/la-fi-spacex- nasa-20161101-story.html)</comment>


Why does London's Moorgate tube station have a mix of logo signage? - <AUTHOR> https://twitter.com/MrTimDunn/status/1065880618662313984 <comment><USER2> Sometimes I don't think we realise or appreciate just how old things are and how they've survived through consistent and conscious effort. A century is beyond the lifetime of most people. A lot of similar-style public transport in the US was practically killed between 1920-1940 with the dawn of the car.

In the UK you might live in a house that is 100 years old, and in London you take a tube train through a tunnel carved out 120 years ago, or something. But it rarely registers that you are using what we in tech would consider way beyond a relic.

Your automated train on the Victoria line was done in the 60s or 70s, the DLR (similarly automated) a decade later. They were so weird at the time that, story has it, the drivers couldn't read a paper in the cabin because it freaked passengers out. Despite the fact they weren't in direct control. Still, automated is weird and it's half a century old.

So what does this say about other historical events that are slipping beyond our collective conscious, like the two world wars? Or even something like 9/11 where there is a whole generation who never saw that?

And what does it say about knowledge? What we keep in our awareness and what we pass on to historians?

<comment><USER3> I currently have my office in a building that was built durinf the year 1265. Still to this date I find this fact fascinating whenever I get reminded about it.

<comment><USER4> Is that in the UK?

</comment></comment></comment><comment><AUTHOR> There are a lot of problems with twitter, but it's great for people who want to share a short thing like this.

From this thread I particularly enjoyed the video of a steam train in an underground station.

I don't know why I enjoy twitter threads like this so much. I hate "factoids" (eg snapple bottle cap real facts), but these twitter threads feel a bit more truthy.

Here's another thread about a woman who ran across Westminster Bridge in less than the time it takes for Big Ben to chime midday. [https://twitter.com/meandmybigmouth/status/10584361322062684...](https://twitter.com/meandmybigmouth/status/1058436132206268416)

That's at least 250 metres (I guess, I don't know where they measure the start and stop of the bridge) in about 55 seconds.

And here's another about the shape of historical cows: "A serious query: were cows in nineteenth century Britain as rectangular shaped as painters envisioned them?" [https://twitter.com/zeenastarbuck/status/1046563793701163010](https://twitter.com/zeenastarbuck/status/1046563793701163010)

<comment><USER5> What exactly am I to do with the link provided, on the desktop? I click on it and I get the first part of of the message 1/6\. There is no intuitive way to continue reading. If I click the replies button, I'm invited to join Twitter. Why should I do that?

As you can imagine, I have the exact opposite feeling, this is the absolute worst way to share a story. Pushing the "network effect moat" pedal to the metal by denying service to non-memebers. Not even evil Facebook takes it to this level (it used to, though).

<comment><USER6> it's text, with images interspersed. it's a perfectly usable way to present information. to read it, you just keep reading - all the information is there on the page. or are you not seeing something that looks like this:

[https://imgur.com/bba37wW](https://imgur.com/bba37wW)

</comment></comment></comment><comment><USER7> While the mixed signage in the thread refers to the Metropolitan line part of Moorgate station, there's a similar mix going on in another part of Moorgate station, specifically the part that's the terminus for the Northern City line ([https://en.wikipedia.org/wiki/Northern_City_Line](https://en.wikipedia.org/wiki/Northern_City_Line)).

It's very anachronistic in terms of London stations - its platform design (and that of most other stations on the subsurface part of the line) is still in the "Network South East" colours and fonts, which for reference hasn't technically existed as a concept since 1994. Just think - a colour scheme now 24 years out of date!

It's a line that isn't on the main Tube Map as it's technically part of the National Rail network and isn't run by Transport for London, even though if you wanted to travel from Moorgate direct to, say, Finsbury Park, the Tube Map would have you believe you need to change at Kings Cross.

(Though mostly this doesn't matter as the vast majority of passengers are commuters from the northern suburbs into the City anyway.)

There's a nice set of photos comparing old with new here, note especially how little it's changed and how unloved this part of the station looks compared with the TfL part. [https://www.flickr.com/photos/60539035@N02/sets/721577011132...](https://www.flickr.com/photos/60539035@N02/sets/72157701113297064)

<comment><USER8> I had to take this line (Moorgate to Enfield from platform 9) during a strike once, and it was the creepiest experience: across all carriages, there was about two non-white people. For a city as diverse as London, this is pretty unusual. It made the train look like some kind of white flight express.

<comment><USER9> London has loads of pockets of areas where diversity is low. Not just white folks, but every ethnicity and religious background will have a pocket of low diversity in London.

I'm not saying it's right, but it does happen.

</comment></comment></comment><comment><USER10> Edward Watkin was amazing. Metropolitan Line? Check. Channel Tunnel? Check. Great Central Railway, the first inter-city continental-gauge railway in Britain? Check[1]. Pioneered a difficult ascent up Snowdon, the highest mountain in Wales? Check[2]. Planned lucrative housing development along public transport infrastructure, known as Metroland? Check[3].

There's a movie in there somewhere.

[1] [https://en.wikipedia.org/wiki/Great_Central_Railway](https://en.wikipedia.org/wiki/Great_Central_Railway)

[2] [https://www.markhorrell.com/blog/2012/snowdon-via-the- watkin...](https://www.markhorrell.com/blog/2012/snowdon-via-the-watkin-path/)

[3] [http://www.crecy.co.uk/a-history-of-the-metropolitan- railway...](http://www.crecy.co.uk/a-history-of-the-metropolitan-railway- metro-land)

</comment><comment><USER11> Reminder to anyone interested in the history of London transport that Geoff Marshall's channel is all about just that [https://www.youtube.com/channel/UCd18OhMfRmjMjzSHP7Zrzmw](https://www.youtube.com/channel/UCd18OhMfRmjMjzSHP7Zrzmw)

<comment><USER12> Geoff and Vicki are awesome. I loved Geoff's series on "Secrets of the [name] line," especially the one that concluded with the Waterloo & City Line where he revealed the little tidbits that had been hidden in the previous videos. (And "Secrets of the Cable Car" was hilarious.)

Vicki also makes an excellent presenter. Her "solo" video about Harry Potter Locations around London, and particularly the tube, was great.

</comment></comment><comment><USER13> Similar things happened in Vienna. The U6 line is completely different from the rest because it was originally a Stadtbahn and not a subway. The rolling stock to this date cannot be used in automated operation at all, has different electrification (overhead wire and not third rail), has lower platforms and still retains many of the old signage.

Originally there was a steam operation on that line as well: [https://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/St...](https://upload.wikimedia.org/wikipedia/commons/thumb/f/fd/Stadtbahn- Wien-vor-Elektrifizierung.jpg/2880px-Stadtbahn-Wien-vor-Elektrifizierung.jpg)

Later they made the line even weirder by running mixed tram and stadtbahn operation: [https://upload.wikimedia.org/wikipedia/commons/6/64/Wien- wvb...](https://upload.wikimedia.org/wikipedia/commons/6/64/Wien-wvb- sl-64-e2-642365.jpg) (tram rolling stock stayed on that line even up to 2008 but were not going into mixed operation any more [https://upload.wikimedia.org/wikipedia/commons/5/5c/U6_Hande...](https://upload.wikimedia.org/wikipedia/commons/5/5c/U6_Handelskai3.JPG))

It's now a proper subway by all accounts but still retains some of its weird history. For instance there is still a track connecting to the tram network so you can sometimes see a subway train go on the tram network for maintenance: [http://www.vormagazin.at/tools/imager/imager.php?file=%2Fmed...](http://www.vormagazin.at/tools/imager/imager.php?file=%2Fmedia%2Fimage%2F1358_1181788731.jpg)

The stations still retain much of the old Stadtbahn architecture and show the old signage more prominently than the new one: [https://upload.wikimedia.org/wikipedia/commons/thumb/3/39/Me...](https://upload.wikimedia.org/wikipedia/commons/thumb/3/39/Metrostacio_Alser_Stra%C3%9Fe.jpg/2880px- Metrostacio_Alser_Stra%C3%9Fe.jpg)

I always find it very interesting when some old things stay around and become integrated into something else and that transition period never really ends. Many transit networks in Europe have history like this and it's fun to rediscover this history.

</comment><comment><USER14> Compiled for easier viewing here: [https://threadreaderapp.com/thread/1065880618662313984.html](https://threadreaderapp.com/thread/1065880618662313984.html)

</comment><comment><USER15> Another excellent BBC4 documentary on the subject, Two Types: The Faces of Britain.

[https://www.bbc.co.uk/programmes/b0903ppd](https://www.bbc.co.uk/programmes/b0903ppd)

</comment><comment><USER16> TIL England tried to copy the Eiffel tower: [https://en.wikipedia.org/wiki/Watkin%27s_Tower](https://en.wikipedia.org/wiki/Watkin%27s_Tower)

<comment><USER15> And succeeded at a much smaller scale

[https://en.m.wikipedia.org/wiki/Blackpool_Tower](https://en.m.wikipedia.org/wiki/Blackpool_Tower)

<comment><USER17> Grimsby's tower is more my style:

[https://en.wikipedia.org/wiki/Grimsby_Dock_Tower](https://en.wikipedia.org/wiki/Grimsby_Dock_Tower)</comment></comment></comment>